This paper describes the development of a robust algorithm for multiobjective optimization, known as robust multiobjective simulated annealing (rMOSA). rMOSA is a simulated annealing based multiobjective optimization algorithm, in which two new mechanisms are incorporated (1) to speed up the process of convergence to attain Pareto front (or a set of nondominating solutions) and (2) to get uniform nondominating solutions along the final Pareto front. A systematic procedure to call the process of choosing a random point in Archive for the perturbation step (in rMOSA) is chosen as the first mechanism to speed up the process of convergence to obtain/attain a final Pareto front, while the other is a systematic procedure to call the process of choosing a most uncrowded solution in Archive for the perturbation step to get a well-crowded uniform Pareto front. First, a Simple MOSA is developed by using the concepts of an archiving procedure, a simple probability function (which is used to set new-pt as current-pt), single parameter perturbation, and a simple annealing schedule. Then, the proposed two new mechanisms are implemented on top of Simple MOSA to develop a robust algorithm for multiobjective optimization (MOO), known as rMOSA. Seven steps involved in the development of rMOSA are thoroughly explained while presenting the algorithm. Four computationally intensive benchmark problems and one simulation-intensive two-objective problem for an industrial FCCU are solved using two newly developed algorithms (rMOSA and Simple MOSA) and two well-known currently existing MOO algorithms (NSGA-II-JG and NSGA-II). Performances of newly developed rMOSA and Simple MOSA (i.e., rMOSA without two new mechanisms) are compared with NSGA-II-JG and NSGA-II, using different metrics available in MOO literature. Newly developed rMOSA is proved to converge to Pareto sets in less number of simulations with well-crowded uniform nondominating solutions in them, for all the problems considered in this study. Hence, rMOSA can be considered as one of the best algorithm for solving computationally intensive and simulation-intensive MOO problems in chemical as well as other fields of engineering.